Original ledger status
SEAM.HORIZON.01
Seam=horizon [I] keystones (pure identities, NO cosmological narrative): (1) the integer 8 in c3=1/(8pi) is OVERDETERMINED and gravitationally aligned: geometry 8=2|mu4| (8pi=|mu4|*2pi seam winding), lattice 8=rank E8=g+n=h(D5)=phi(30)=det R, gravity 8pi=Hawking/Einstein coeff (G_uv=8pi T_uv) => if seam=horizon, c3 is gravitationally forced and the gravitational 8 MUST equal the lattice/geometry 8 (it does). Both pi-coeffs are 2pi*integer: phi_tree=1/(6pi),6=2 N_fam (Gauss-Bonnet); c3=1/(8pi),8=2|mu4|; phi_tree=(|mu4|/N_fam)c3=(4/3)c3. (2) ONE transfer operator for BOTH sectors: boundary transport spec {1,(2/3)^6,(1/3)^6}; lambda2=(2/3)^6 = SM flavor gap eigenvalue (Delta=-log(2/3)^6=6 log 3/2=2.4328, tfpt_2) = horizon Page recovery rate (I_n~lambda2^n, Appendix H). Cusp weights {0,1/3,2/3} at 4 mu4-punctures = boundary data. Supporting: S_BH=A/|mu4|, 128 c3^4=1/(32 pi^4), T_dS coeff 16=|mu4|^2. The cyclic self-reproduction reading is [P] interpretation NOT included here
Recorded status: Identity [I]
Dependencies, status detail and source
Canonical status: Identity [I]
Dependencies: BND.GLUE.01; v6; v8; v10; tfpt_2 transport spec
Scripts: v54_seam_horizon_keystones.py
Location: tfpt_3;tfpt_horizon_readouts
Original CSV, line 135Original ledger status
QGEO.DTN.01
SUBCLAIM 2 OF QGEO.ENERGY.02 TACKLED -- 'the raw RP-seam DtN is RP-definable' (external-review next-lever 2026-06-14): a REDUCTION, not a closure. (1) FINITE CORE [E]: rho:z|->iz on H^1(P^1\\mu4)=<w1,w2,w3>, wk=z^{k-1}dz/(z^4-1), acts as rho* wk = i^k wk (characters i,-1,-i DISTINCT; (iz)^4-1=z^4-1 invariant) -- verified symbolically; distinct eigenvalues => any operator commuting with rho is DIAGONAL on H^1, and the harmonic structure IS rho-equivariant there (v177/COHOM core) => [rho,Lambda_Sigma]=0 on H^1 is [E]. (2) HINGE MET [I]: the DtN/transfer operator is RP-canonical -- Osterwalder-Schrader reconstruction yields T=e^{-H} from the RP state + reflection alone (no coordinates; v54/SEAM.HORIZON.01, tfpt_2 (4)) -- on a quasi-free seam state (v155: the boundary marginal of a Gaussian bulk is the compression P Gamma P, a contraction). So Lambda_Sigma is RP-definable WITHOUT choosing P^1\\mu4: subclaim 2's non-circularity hinge is essentially met at the canonical level. (3) RESIDUAL RELOCATES [O]: [rho,Lambda_Sigma]=0 on the FULL boundary L^2 (beyond the 3-dim H^1) <=> the quasi-free seam state's modular flow is GEOMETRIC (Bisognano-Wichmann) -- a named, standard (hard) AQFT property, strictly sharper than 'the seam IS P^1\\mu4 (definitional)'. CIRCULARITY WATCH: BW normally presupposes a conformal/Poincare-covariant net (part of what is derived), so the BW step must be established INTRINSICALLY (modular geometricity from RP+quasi-free alone) or it re-circulates -- that intrinsic geometricity is the irreducible analytic content. VERDICT: subclaim 2's hinge met + finite core [E] => QGEO.SYM.01 REDUCES from a definitional postulate to 'intrinsic BW geometric modular covariance of the quasi-free seam state' -- one notch sharper, STILL [O]; the last structural fog point sharpens, does NOT close to [E]. Python-only (H^1 commutation is exact Moebius-symbolic like v177; reduction is structural)
Recorded status: Geometric premise [O] (reduction: subclaim-2 hinge met, finite core [E], bedrock -> BW modular)
Dependencies, status detail and source
Canonical status: Geometric [O]: subclaim 2 (raw-seam DtN RP-definability) met at the canonical OS level + finite core [E]; QGEO.SYM.01 reduces to intrinsic Bisognano-Wichmann modular covariance of the quasi-free seam state -- sharper, still [O], not closed
Dependencies: QGEO.ENERGY.02; QGEO.SYM.01; QGEO.TREE.01; SEAM.HORIZON.01; v177_seam_marking_kernel.py; v155_quasifree_boundary.py; v54_seam_horizon_keystones.py
Scripts: v194_raw_seam_dtn_rp.py
Location: tfpt_research_contracts
Original CSV, line 268